Lecture28-Notes - ME 382 Lecture 28 1 E FFECT OF VARIABLE...

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Unformatted text preview: ME 382 Lecture 28 1 E FFECT OF VARIABLE STRESSES ON FATIGUE LIFE • Loading history may not be uniform • To estimate approximate life-times use Palmgren 1920 − Miner 1945 Rule : N i N f i i ∑ = 1 (often called Miner’s rule) where, N i = # cycles in load block i N fi = # cycles to failure for constant cycling of type in load block i Note : All these fatigue laws are empirical . They do not always work, and should be used with caution! Examples of fatigue calculations Example 1 A loading sequence consists of Block 1. 20 cycles ( σ m = 0 MPa, σ a = 200 MPa) Block 2. 5 cycles ( σ m = 0 MPa, σ a = 250 MPa) How many times can this be repeated until failure using a 2024 Al alloy for which σ a N f 0.102 = 839 MPa and σ Y = 303 MPa Step (i): Block 1: σ m = 0 ⇒ OK to use Basquin’s Law σ max = 200 MPa; σ min = -200 MPa Check for yield: ˜ σ H < σ Y ⇒ no yield Block 2: σ m = 0 ⇒ OK to use Basquin’s Law σ max = 250 MPa; σ min = -250 MPa Check for yield: ˜ σ H < σ Y ⇒ no yield ME 382 Lecture 28 2 Step (ii): N f 1 0.102 = 839/200 N f 2 0.102 = 839/250 ∴ N f 1 = 1.27 × 10 6 cycles ∴ N f 2 = 1.43 × 10 5 cycles Step (iii): Number of loading blocks to failure = B f Miner’s Law ⇒ B f 20 1.27 × 10 6 + 5 1.43 × 10 5 Λ Ν Ξ Π = 1 ∴ B f 5.07 × 10 − 5 ( ) = 1 ∴ B f = 2.0 × 10 4 Example 2: • Fatigue life of aluminum alloy given by...
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Lecture28-Notes - ME 382 Lecture 28 1 E FFECT OF VARIABLE...

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